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Boolean Union and Intersection working

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hkrish 2013-04-18 20:27:19 +02:00
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.exrc Normal file
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Boolean.js Normal file
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/*!
*
* Vector boolean operations on paperjs objects
* This is mostly written for clarity (I hope it is clear) and compatibility,
* not optimised for performance, and has to be tested heavily for stability.
* (Looking up to Java's Area path boolean algorithms for stability,
* but the code is too complex —mainly because the operations are stored and
* enumerable, such as quadraticCurveTo, cubicCurveTo etc.; and is largely
* undocumented to directly adapt from)
*
* Supported
* - paperjs Path objects
* - Boolean Union operations
* - Boolean Intersection operations
* - handles path complexity quite nicely
*
* Not supported yet ( which I would like to see supported )
* - Compound Paths as input ( however compound paths are correctly handled in the output )
* - Self-intersecting Paths
* - Boolean Subtraction operation ( depends on compound paths as input )
* - Paths are clones of each other that ovelap exactly on top of each other!
*
* In the Not-supported-yet list, the first three can be easily implemented,
* as for the last point, I need help! Thanks! :)
*
* ------
* Harikrishnan Gopalakrishnan
* http://hkrish.com/playground/paperbool.html
*
* ------
* Paperjs
* Copyright (c) 2011, Juerg Lehni & Jonathan Puckey
* http://paperjs.org/license/
*
*/
/**
* BooleanOps defines the boolean operator functions to use.
* A boolean operator is a function f( link:Link, isInsidePath1:Boolean, isInsidePath2:Boolean ) :
* should return a Boolean value indicating whether to keep the link or not.
* return true - keep the path
* return false - discard the path
*/
var BooleanOps = {
Union: function( lnk, isInsidePath1, isInsidePath2 ){
if( isInsidePath1 || isInsidePath2 ){
return false;
}
return true;
},
Intersection: function( lnk, isInsidePath1, isInsidePath2 ){
if( !isInsidePath1 && !isInsidePath2 ){
return false;
}
return true;
}
};
/**
* The datastructure for boolean computation:
* Graph - List of Links
* Link - Connects 2 Nodes, represents a Curve
* Node - Connects 2 Links, represents a Segment
*/
var NORMAL_NODE = 1;
var INTERSECTION_NODE = 2;
var IntersectionID = 1;
var UNIQUE_ID = 1;
/**
* Nodes in the graph are analogous to Segment objects
* with additional linkage information to track intersections etc.
* (enough to do a complete graph traversal)
* @param {Point} _point
* @param {Point} _handleIn
* @param {Point} _handleOut
* @param {Any} _id
*/
function Node( _point, _handleIn, _handleOut, _id ){
this.id = _id;
this.type = NORMAL_NODE;
this.point = _point;
this.handleIn = _handleIn; // handleIn
this.handleOut = _handleOut; // handleOut
this.linkIn = null; // aka linkIn
this.linkOut = null; // linkOut
this.uniqueID = ++UNIQUE_ID;
// In case of an intersection this will be a merged node.
// And we need space to save the "other Node's" parameters before merging.
this.idB = null;
// this.pointB = this.point; // point should be the same
this.handleBIn = null;
this.handleBOut = null;
this.linkBIn = null;
this.linkBOut = null;
this._segment = null;
this.getSegment = function( recalculate ){
if( this.type === INTERSECTION_NODE && recalculate ){
// point this.linkIn and this.linkOut to those active ones
// also point this.handleIn and this.handleOut to correct in and out handles
// If a link is null, make sure the corresponding handle is also null
this.handleIn = (this.linkIn)? this.handleIn : null;
this.handleOut = (this.linkOut)? this.handleOut : null;
this.handleBIn = (this.linkBIn)? this.handleBIn : null;
this.handleBOut = (this.linkBOut)? this.handleBOut : null;
// Select the valid links
this.linkIn = this.linkIn || this.linkBIn; // linkIn
this.linkOut = this.linkOut || this.linkBOut; // linkOut
// Also update the references in links to point to "this" Node
this.linkIn.nodeOut = this; // linkIn.nodeEnd
this.linkOut.nodeIn = this; // linkOut.nodeStart
this.handleIn = this.handleIn || this.handleBIn;
this.handleOut = this.handleOut || this.handleBOut;
}
this._segment = this._segment || new Segment( this.point, this.handleIn, this.handleOut );
return this._segment;
};
}
/**
* Links in the graph are analogous to CUrve objects
* @param {Node} _nodeIn
* @param {Node} _nodeOut
* @param {Any} _id
*/
function Link( _nodeIn, _nodeOut, _id ) {
this.id = _id;
this.nodeIn = _nodeIn; // nodeStart
this.nodeOut = _nodeOut; // nodeEnd
this.nodeIn.linkOut = this; // nodeStart.linkOut
this.nodeOut.linkIn = this; // nodeEnd.linkIn
this._curve = null;
this.intersections = [];
// for reusing the paperjs function we need to (temperorily) build a Curve object from this Link
// for performance reasons we cache it.
this.getCurve = function() {
this._curve = this._curve || new Curve( this.nodeIn.getSegment(), this.nodeOut.getSegment() );
return this._curve;
};
}
/**
* makes a graph. Only works on paths, for compound paths we need to
* make graphs for each of the child paths and merge them.
* @param {Path} path
* @param {Integer} id
* @return {Array} Links
*/
function makeGraph( path, id ){
var graph = [];
var segs = path.segments, prevNode = null, firstNode = null, nuLink, nuNode;
for( i = 0, l = segs.length; i < l; i++ ){
var nuSeg = segs[i].clone();
nuNode = new Node( nuSeg.point, nuSeg.handleIn, nuSeg.handleOut, id );
if( prevNode ) {
nuLink = new Link( prevNode, nuNode, id );
graph.push( nuLink );
}
prevNode = nuNode;
if( !firstNode ){
firstNode = nuNode;
}
}
// the path is closed
nuLink = new Link( prevNode, firstNode, id );
graph.push( nuLink );
return graph;
}
/**
* Calculates the Union of two paths
* Boolean API.
* @param {Path} path1
* @param {Path} path2
* @return {CompoundPath} union of path1 & path2
*/
function boolUnion( path1, path2 ){
return computeBoolean( path1, path2, BooleanOps.Union );
}
/**
* Calculates the Intersection between two paths
* Boolean API.
* @param {Path} path1
* @param {Path} path2
* @return {CompoundPath} Intersection of path1 & path2
*/
function boolIntersection( path1, path2 ){
return computeBoolean( path1, path2, BooleanOps.Intersection );
}
/**
* Actual function that computes the boolean
* @param {Path} _path1 (cannot be self-intersecting at the moment)
* @param {Path} _path2 (cannot be self-intersecting at the moment)
* @param {BooleanOps type} operator
* @return {CompoundPath} boolean result
*/
function computeBoolean( _path1, _path2, operator ){
IntersectionID = 1;
UNIQUE_ID = 1;
// The boolean operation may modify the original paths
var path1 = _path1.clone();
var path2 = _path2.clone();
if( !path1.clockwise ){ path1.reverse(); }
if( !path2.clockwise ){ path2.reverse(); }
// Prepare the graphs. Graphs are list of Links that retains
// full connectivity information. The order of links in a graph is not important
// That allows us to sort and merge graphs and 'splice' links with their splits easily.
// Also, this is the place to resolve self-intersecting paths
var graph = makeGraph( path1, 1 );
var graph2 = makeGraph( path2, 2 );
// Merge the two graphs. Since we have unique id's for each Link and Node,
// retrieveing the original graphs is rather simple.
graph = graph.concat( graph2 );
// Sort function to sort intersections according to the 'parameter'(t) in a link (curve)
function ixSort( a, b ){ return a._parameter - b._parameter; }
var i, j, k, l, lnk, crv, node, nuNode, leftLink, rightLink;
/*
* Pass 1:
* Calculate the intersections for all graphs
* TODO: test if this takes are of self intersecting paths - NO
* And since it doesn't take self-intersecting curves, we need to only calculate
* intersections if the "id" of the links differ.
* The rest of the algorithm can easily be modified to resolve self-intersections
*/
for ( i = graph.length - 1; i >= 0; i--) {
var c1 = graph[i].getCurve();
var v1 = c1.getValues();
for ( j = i -1; j >= 0; j-- ) {
if( graph[j].id === graph[i].id ){ continue; }
var c2 = graph[j].getCurve();
var v2 = c2.getValues();
var loc = [];
Curve._addIntersections( v1, v2, loc );
if( loc.length ){
for (k = 0, l=loc.length; k<l; k++) {
var loc1 = loc[k].clone();
loc1._intersectionID = loc[k]._intersectionID;
loc1._parameter = c1.getNearestLocation( loc[k] ).parameter; // For sorting on curve1
graph[i].intersections.push( loc1 );
var loc2 = loc[k].clone();
loc2._intersectionID = loc[k]._intersectionID;
loc2._parameter = c2.getNearestLocation( loc[k] ).parameter; // For sorting on curve2
graph[j].intersections.push( loc2 );
}
}
}
}
/*
* Pass 2:
* Walk the graph, sort the intersections on each individual link.
* for each link that intersects with another one, replace it with new split links.
*/
for ( i = graph.length - 1; i >= 0; i--) {
if( graph[i].intersections.length ){
var ix = graph[i].intersections;
ix.sort( ixSort );
// Remove the graph link, this link has to be split and replaced with the splits
lnk = graph.splice( i, 1 )[0];
for (j =0, l=ix.length; j<l && lnk; j++) {
var splitLinks = [];
crv = lnk.getCurve();
// We need to recalculate parameter after each curve split
// This operation (except for recalculating the curve parameter),
// is fairly similar to Curve.split method, except that it operates on Node and Link objects.
var param = crv.getNearestLocation( ix[j] ).parameter;
if( param === 0.0 || param === 1.0) {
// Intersection falls on an existing node
// there is no need to split the link
nuNode = ( param === 0.0 )? lnk.nodeIn : lnk.nodeOut;
nuNode.type = INTERSECTION_NODE;
nuNode._intersectionID = ix[j]._intersectionID;
if( param === 1.0 ){
leftLink = null;
rightLink = lnk;
} else {
leftLink = lnk;
rightLink = null;
}
} else {
var parts = Curve.subdivide(crv.getValues(), param);
var left = parts[0];
var right = parts[1];
// Make new link and convert handles from absolute to relative
// TODO: check if link is linear and set handles to null
var ixPoint = new Point( left[6], left[7] );
nuNode = new Node( ixPoint, new Point(left[4] - ixPoint.x, left[5] - ixPoint.y),
new Point(right[2] - ixPoint.x, right[3] - ixPoint.y), lnk.id );
nuNode.type = INTERSECTION_NODE;
nuNode._intersectionID = ix[j]._intersectionID;
// clear the cached Segment on original end nodes and Update their handles
lnk.nodeIn._segment = null;
var tmppnt = lnk.nodeIn.point;
lnk.nodeIn.handleOut = new Point( left[2] - tmppnt.x, left[3] - tmppnt.y );
lnk.nodeOut._segment = null;
tmppnt = lnk.nodeOut.point;
lnk.nodeOut.handleIn = new Point( right[4] - tmppnt.x, right[5] - tmppnt.y );
// Make new links after the split
leftLink = new Link( lnk.nodeIn, nuNode, lnk.id );
rightLink = new Link( nuNode, lnk.nodeOut, lnk.id );
}
// Add the first split link back to the graph, since we sorted the intersections
// already, this link should contain no more intersections to the left.
if( leftLink ){
graph.splice( i, 0, leftLink );
}
// continue with the second split link, to see if
// there are more intersections to deal with
lnk = rightLink;
}
// Add the last split link back to the graph
if( lnk ){
graph.splice( i, 0, lnk );
}
}
}
/**
* Pass 3:
* Merge matching intersection Node Pairs (type is INTERSECTION_NODE &&
* a._intersectionID == b._intersectionID )
*
* Mark each Link(Curve) according to whether it is
* case 1. inside Path1 ( and only Path1 )
* 2. inside Path2 ( and only Path2 )
* 3. inside both ( fully contained holes that completely overlap )
* 4. outside (normal case)
*
* Take a test function "operator" which will discard links
* according to the above
* * Union -> discard cases 1, 2 and 3
* * Intersection -> discard case 4
* * Path1-Path2 -> discard cases 2, 3[Path1] and 4[Path2]‡
* * Path2-Path1 -> discard cases 1, 3[Path2] and 4[Path1]
* ‡ - 4[Path2] means curves of case 4 that belongs to Path2
*/
// step 1: discard invalid links according to the boolean operator
for ( i = graph.length - 1; i >= 0; i--) {
lnk = graph[i];
crv = lnk.getCurve();
// var midPoint = new Point(lnk.nodeIn.point);
var midPoint = crv.getPoint( 0.5 );
var insidePath1 = (lnk.id === 1 )? false : path1.contains( midPoint );
var insidePath2 = (lnk.id === 2 )? false : path2.contains( midPoint );
if( !operator( lnk, insidePath1, insidePath2 ) ){
// lnk = graph.splice( i, 1 )[0];
lnk.INVALID = true;
lnk.nodeIn.linkOut = null;
lnk.nodeOut.linkIn = null;
}
}
// step 2: Match nodes according to their _intersectionID and merge them together
var len = graph.length;
while( len-- ){
node = graph[len].nodeIn;
if( node.type === INTERSECTION_NODE ){
var otherNode = null;
for (i = len - 1; i >= 0; i--) {
var tmpnode = graph[i].nodeIn;
if( tmpnode._intersectionID === node._intersectionID &&
tmpnode.uniqueID !== node.uniqueID ) {
otherNode = tmpnode;
break;
}
}
if( otherNode ) {
//Check if it is a self-intersecting Node
if( node.id === otherNode.id ){
// Swap the outgoing links, this will resolve a knot and create two paths,
// the portion of the original path on one side of a self crossing is counter-clockwise,
// so one of the resulting paths will also be counter-clockwise
var tmp = otherNode.linkOut;
otherNode.linkOut = node.linkOut;
node.linkOut = tmp;
tmp = otherNode.handleOut;
otherNode.handleOut = node.handleOut;
node.handleOut = tmp;
node.type = otherNode.type = NORMAL_NODE;
node._intersectionID = null;
node._segment = otherNode._segment = null;
} else {
// Merge the nodes together, by adding this node's information to the other node
otherNode.idB = node.id;
otherNode.handleBIn = node.handleIn;
otherNode.handleBOut = node.handleOut;
otherNode.linkBIn = node.linkIn;
otherNode.linkBOut = node.linkOut;
otherNode._segment = null;
if( node.linkIn ){ node.linkIn.nodeOut = otherNode; }
if( node.linkOut ){ node.linkOut.nodeIn = otherNode; }
// Clear this node's intersectionID, so that we won't iterate over it again
node._intersectionID = null;
}
}
}
}
// Final step: Retrieve the resulting paths from the graph
var boolResult = new CompoundPath();
var firstNode = true, nextNode;
while( firstNode ){
firstNode = nextNode = null;
len = graph.length;
while( len-- ){
if( !graph[len].INVALID && !graph[len].nodeIn.visited && !firstNode ){
firstNode = graph[len].nodeIn;
break;
}
}
if( firstNode ){
var path = new Path();
path.add( firstNode.getSegment( true ) );
firstNode.visited = true;
nextNode = firstNode.linkOut.nodeOut;
while( firstNode.uniqueID !== nextNode.uniqueID ){
path.add( nextNode.getSegment( true ) );
nextNode.visited = true;
nextNode = nextNode.linkOut.nodeOut;
}
path.closed = true;
// path.clockwise = true;
boolResult.addChild( path );
}
}
boolResult = boolResult.reduce();
return boolResult;
}
// Same as the paperjs' Numerical class,
// added here because I can't access the original from this scope
var Numerical = {
TOLERANCE : 10e-6
};
// paperjs' Curve._addIntersections modified to return just intersection Point with a
// unique id.
paper.Curve._addIntersections = function(v1, v2, locations) {
var bounds1 = Curve.getBounds(v1),
bounds2 = Curve.getBounds(v2);
if (bounds1.touches(bounds2)) {
// See if both curves are flat enough to be treated as lines.
if (Curve.isFlatEnough(v1, /*#=*/ Numerical.TOLERANCE) &&
Curve.isFlatEnough(v2, /*#=*/ Numerical.TOLERANCE)) {
// See if the parametric equations of the lines interesct.
var point = new Line(v1[0], v1[1], v1[6], v1[7], false)
.intersect(new Line(v2[0], v2[1], v2[6], v2[7], false),
// Filter out beginnings of the curves, to avoid
// duplicate solutions where curves join.
true, false);
if (point){
point._intersectionID = IntersectionID++;
locations.push( point );
}
} else {
// Subdivide both curves, and see if they intersect.
var v1s = Curve.subdivide(v1),
v2s = Curve.subdivide(v2);
for (var i = 0; i < 2; i++)
for (var j = 0; j < 2; j++)
this._addIntersections(v1s[i], v2s[j], locations);
}
}
return locations;
};

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boolean1.js
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project.currentStyle.fillColor = 'black';
var path11 = new Path.Rectangle([100, 100], [100, 100]);
var path21 = new Path.Rectangle([50, 30], [100, 100]);
var newPath = new Path();
path11.style.fillColor = 'rgb( 71, 91, 98 )'
path21.style.fillColor = 'rgb( 129, 144, 144 )'
// onFrame = function( event ) {
path21.rotate( 148 );
var path1 = path11.clone();
var path2 = path21.clone();
newPath.removeSegments();
// Intersections of path1 with path2
var ixs = path1.getIntersections( path2 );
// TODO for both paths, first sort ixs according to curveOffset,
// so that, insert order is correct
ixs.forEach( function( item, index ){
// T
console.log( item.curveOffset )
var newSeg1 = new Segment( item.point );
var newSeg2 = new Segment( item.point );
newSeg1._ixOtherSeg = newSeg2;
newSeg2._ixOtherSeg = newSeg1;
path1.insertSegment( item.curve.segment1.index + 1, newSeg1 );
path2.insertSegment( item._ixCurve.segment1.index + 1, newSeg2 );
});
// console.log( path2.segments )
var startSeg = path1.firstSegment;
// TODO Make sure, if path1 is not completely inside path2
while( path2.contains( startSeg.point ) ) {
startSeg = startSeg.next;
}
// path2.firstSegment.selected = path2.firstSegment.next.selected = true;
// path1.firstSegment.selected = path1.firstSegment.next.selected = true;
console.log( path1.isClockwise() )
console.log( path2.isClockwise() )
// path2.reverse()
// startSeg.selected = true;
var curSeg;
var count = 1;
var ixswitch = true;
while( curSeg !== startSeg ) {
if( !curSeg ) {
curSeg = startSeg;
}
if( curSeg._ixOtherSeg ){
curSeg = curSeg._ixOtherSeg;
ixswitch = !ixswitch
}
newPath.addSegment( new Segment( curSeg ) );
var text = new PointText( curSeg.point - [ 5, 5 ] );
text.justification = 'center';
if( ixswitch ) {
text.fillColor = 'black';
}else{
text.fillColor = 'blue';
}
text.content = count.toString();
count++;
curSeg = curSeg.next;
}
newPath.translate( [200, 0] );
newPath.style.fillColor = 'rgb( 209, 28, 36 )';
newPath.selected = true;
// path1.remove();
// path2.remove();
// }
// path1.selected = true;
// path1.selected = true;

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boolean2.js
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project.currentStyle.fillColor = 'black';
var path11 = new Path.Circle([80, 80], 50);
// var path11 = new Path.Rectangle([100, 100], [100, 100]);
var path21 = new Path.Rectangle([100, 100], [100, 100]);
// var path21 = new Path.Polygon
var newPath = new Path();
path11.style.fillColor = 'rgb( 71, 91, 98 )'
path21.style.fillColor = 'rgb( 129, 144, 144 )'
// onFrame = function( event ) {
path21.rotate( 1 );
newPath.removeSegments();
var path1 = path11.clone();
var path2 = path21.clone();
// console.log(path1.isClockwise())
// console.log(path2.isClockwise())
// Intersections of path1 with path2
var ixs = path1.getIntersections( path2 );
// TODO for both paths, first sort ixs according to curveOffset,
// so that, insert order is correct
if( ixs.length > 0 ) {
ixs.forEach( function( item, index ){
var newSeg1 = new Segment( item.point );
var newSeg2 = new Segment( item.point );
newSeg1._ixCurveOffset = item.curveOffset;
newSeg2._ixCurveOffset = item._ixLocation.curveOffset;
newSeg1._ixOtherSeg = newSeg2;
newSeg2._ixOtherSeg = newSeg1;
if( item.curve.segment1._ixPoints === undefined ){
item.curve.segment1._ixPoints = [ newSeg1 ];
} else {
item.curve.segment1._ixPoints.push( newSeg1 );
}
if( item._ixLocation.curve.segment1._ixPoints === undefined ){
item._ixLocation.curve.segment1._ixPoints = [ newSeg2 ];
} else {
item._ixLocation.curve.segment1._ixPoints.push( newSeg2 );
}
});
// path1.segments.forEach( function( item, index ){
// if( item._ixPoints ) {
// if( item._ixPoints.length > 1 ) {
// item._ixPoints.sort( compare_ixPoints );
// }
// path1.insertSegments( item.index + 1, item._ixPoints );
// item._ixPoints = undefined;
// }
// });
// path2.segments.forEach( function( item, index ){
// console.log(item._ixPoints)
// if( item._ixPoints ) {
// if( item._ixPoints.length > 1 ) {
// item._ixPoints.sort( compare_ixPoints );
// }
// path2.insertSegments( item.index + 1, item._ixPoints );
// item._ixPoints = undefined;
// }
// });
// TODO make sure path is closed
// Walk the segments in path1, backwards (counter-clockwise)
var pathSeg = path1.lastSegment;
do{
if( pathSeg._ixPoints ) {
if( pathSeg._ixPoints.length > 1 ) {
pathSeg._ixPoints.sort( compare_ixPoints );
}
path1.insertSegments( pathSeg.index + 1, pathSeg._ixPoints );
pathSeg._ixPoints = undefined;
}
pathSeg = pathSeg.previous;
} while ( pathSeg !== path1.lastSegment );
// Walk the segments in path2, backwards (counter-clockwise)
var pathSeg = path2.lastSegment;
do {
if( pathSeg._ixPoints ) {
if( pathSeg._ixPoints.length > 1 ) {
pathSeg._ixPoints.sort( compare_ixPoints );
}
path2.insertSegments( pathSeg.index + 1, pathSeg._ixPoints );
pathSeg._ixPoints = undefined;
}
pathSeg = pathSeg.previous;
} while ( pathSeg !== path2.lastSegment );
// TODO Make sure, if path1 is not completely inside path2.
// TODO. This part will differ for different boolean ops.
// For Union
var startSeg = path1.firstSegment;
while( path2.contains( startSeg.point ) || startSeg._ixOtherSeg ) {
startSeg = startSeg.next;
}
// path11.segments[startSeg.index].selected = true;
// startSeg.selected = true;
var curSeg;
var count = 1;
var ixswitch = true;
do {
if( !curSeg ) {
curSeg = startSeg;
}
if( curSeg._ixOtherSeg ){
curSeg = curSeg._ixOtherSeg;
ixswitch = !ixswitch
}
newPath.addSegment( new Segment( curSeg ) );
// var text = new PointText( curSeg.point - [ 5, 5 ] );
// text.justification = 'center';
// if( ixswitch ) {
// text.fillColor = 'black';
// }else{
// text.fillColor = 'blue';
// }
// text.content = count.toString();
count++;
curSeg = curSeg.next;
} while( curSeg !== startSeg && count < 50);
// console.log(count);
// annotateSegments( path1, 5, '#f00' )
// annotateSegments( path2, -5, '#000' )
newPath.closePath()
newPath.translate( [200, 0] );
newPath.style.fillColor = 'rgb( 209, 28, 36 )';
newPath.fullySelected = true;
}
// path1.remove();
// path2.remove();
// }
// path1.selected = true;
// path2.selected = true;
// Sort new intersection points according to their
// distance along the curve, so that when we
// insert them in to the respective paths, the orientation
// of the path is maintained ( in out case clockwise )
function compare_ixPoints( a, b ) {
if( a._ixCurveOffset < b._ixCurveOffset ) {
return -1
} else if( a._ixCurveOffset > b._ixCurveOffset ){
return 1;
} else {
// This shouldn't happen?!
return 0;
}
}
// For debugging: Show a number next to each segment ina path
function annotateSegments( p, d, c ) {
var count = 0;
p.segments.forEach( function( item, index ){
var text = new PointText( item.point - [ d, d ] );
text.style.fillColor = c;
text.justification = 'center';
text.content = count.toString();
count++;
});
}

166
boolean3.js
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@ -1,166 +0,0 @@
project.currentStyle.fillColor = 'black';
// var path11 = new Path.Circle([95, 95], 50);
// var path21 = new Path.Rectangle([100, 100], [100, 100]);
// var path11 = new Path.Rectangle([100, 100], [100, 100]);
// var path21 = new Path.Polygon
var path11 = new Path.Star(new Point(260, 250), 10, 50, 150);
var path21 = new Path.Star(new Point(350, 250), 10, 70, 250);
// path11.smooth();
// path21.smooth();
path11.style.fillColor = 'rgb( 71, 91, 98 )'
path21.style.fillColor = 'rgb( 129, 144, 144 )'
function compare_ixPoints( a, b ) {
if( a.curveOffset < b.curveOffset ) {
return -1
} else if( a.curveOffset > b.curveOffset ){
return 1;
} else {
// This shouldn't happen?!
return 0;
}
}
Path.prototype.getUnion = function( other ) {
var path1 = this.clone();
var path2 = other.clone();
// TODO do the necessary checks here.
if( !path1.isClockwise() ) path1.reverse();
if( !path2.isClockwise() ) path2.reverse();
console.time("Lines");
var ixs = path1.getIntersections( path2 );
console.timeEnd("Lines");
console.time("sort");
ixs.sort( compare_ixPoints );
console.timeEnd("sort");
// console.log( ixs.length )
for (var i = 0, l = ixs.length; i < l; i++) {
for (var j = i + 1, l = ixs.length; j < l; j++) {
if(ixs[i].point == ixs[j].point &&
ixs[i].curve.index === ixs[j].curve.index &&
ixs[i]._ixLocation.curve.index === ixs[j]._ixLocation.curve.index ){
ixs[i]._ixdup = true;
}
}
}
var counter = 0;
if( ixs.length > 1 ){
ixs.forEach( function( item, index ){
if(item._ixdup) return;
var crv1 = item.divide();
var crv2 = item._ixLocation.divide();
if( !crv1 ) {
if( item.parameter === 1 ){
crv1 = item.curve.next;
} else {
crv1 = item.curve;
}
}
if( !crv2 ) {
console.log( item._ixLocation )
// TODO if _ixLocation.parameter is null
// patch the _addIntersections method,
// to intersect the curve back again at that point
if( item._ixLocation.parameter === 1 ){
crv2 = item._ixLocation.curve.next;
} else {
crv2 = item._ixLocation.curve;
}
}
annotateSegment(crv2.segment1, -10, "#000", false, counter++)
crv1.segment1._ixLink = crv2.segment1;
crv2.segment1._ixLink = crv1.segment1;
});
// annotateSegments( path1, 5, '#000', true )
// annotateSegments( path2, -5, '#00f' )
// path1.fullySelected = true;
// path2.fullySelected = true;
var newPath = new Path(),
startSeg = path1.firstSegment,
curSeg, loopCut = 0;
while( path2.contains( startSeg.point ) || startSeg._ixLink ) {
startSeg = startSeg.next;
}
annotateSegment( startSeg, -5, "#0ff" )
do {
if( !curSeg ) {
curSeg = startSeg;
}
if( curSeg._ixLink ){
newPath.addSegment( new Segment( curSeg.point, curSeg.handleIn, curSeg._ixLink.handleOut) );
console.log( "S - " + curSeg.index + " -> " + curSeg._ixLink.index )
curSeg = curSeg._ixLink;
} else {
newPath.addSegment( new Segment( curSeg ) );
}
loopCut++;
curSeg = curSeg.next;
} while( curSeg !== startSeg && loopCut < 50);
newPath.closePath();
// newPath.style.fillColor = null
newPath.translate( [500, 0] )
annotateSegments( newPath , -5, '#0f0' );
} else {
// TODO one path is either completely inside
// or outside the other one.
}
// Debug code
// console.log( newPath.segments.length );
// annotateSegments( path1, 5, '#000', true )
// path1.fullySelected = true;
// annotateSegments( path2, -5, '#00f' )
// path2.fullySelected = true;
// path1.selected = true;
path2.selected = true;
}
path11.getUnion( path21 )
// For debugging: Show a number next to each segment ina path
function annotateSegments( p, d, c, hiLink ) {
hiLink = hiLink || false;
p.segments.forEach( function( item, index ){
annotateSegment( item, d, c, hiLink )
});
}
function annotateSegment( s, d, c, hiLink , txt) {
hiLink = hiLink || false;
var text = new PointText( s.point - [ d, d ] );
text.style.fillColor = c;
text.justification = 'center';
if( txt === undefined )
text.content = s.index.toString();
else
text.content = txt;
if( hiLink && s._ixLink) {
annotateSegment( s._ixLink, d - 5, '#f00', false )
}
}
function markpoint( p ) {
new Path.Circle(p, 2).style = { strokeColor: '#f0f', fillColor: '#000'}
}
// markpoint( [236.34995495235776, 152.72369685178597 ])

39
booleanStudy.html
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@ -1,13 +1,44 @@
<!DOCTYPE html> <!DOCTYPE html>
<html> <html>
<head> <head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <meta charset="utf-8">
<title>Boolean Study</title> <title>Boolean Study</title>
<link rel="stylesheet" href="../dist/style.css">
<script type="text/javascript" src="../dist/paper.js"></script> <script type="text/javascript" src="../dist/paper.js"></script>
<script type="text/paperscript" canvas="canvas" src="boolean3.js"></script> <script type="text/javascript" src="Boolean.js"></script>
<script type="text/javascript" src="booleanTests.js"></script>
<style>
body { height: 100%; overflow: auto; }
#container { display: block; width: 800px; margin: 0 auto 50px; }
h1, h3 { font-family: 'Helvetica Neue'; font-weight: 300; margin: 50px 0 20px; }
footer{display: block; width: 800px; height: 100px; margin: 30px auto; color: #999; }
footer p { font-family: 'Helvetica Neue'; font-style: italic; font-weight: 300; }
canvas { cursor: crosshair; width: 100%; height: 220px; margin: 5px 0;}
.error { color: #a00; } .hide{ display: none; }
</style>
</head> </head>
<body> <body>
<canvas id="canvas" resize></canvas> <div id="container">
<h1>paperjs - Boolean Tests</h1>
<button id="testStart" value="Start tests" onClick="runTests();">Start tests</button>
</div>
<footer>
<p>Vector boolean operations on paperjs objects. <br />
Still under development, mostly written for clarity and compatibility,
not optimised for performance, and has to be tested heavily.</p>
<p>--<br />
hari</p>
</footer>
<svg class="hide" version="1.1" id="glyphsys" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
width="200px" height="200px" viewBox="0 0 200 200" enable-background="new 0 0 200 200" xml:space="preserve">
<path fill="none" d="M68.836,146.216c8.889,5.698,21.647,10.021,35.324,10.021c20.283,0,32.142-10.689,32.142-26.203
c0-14.122-8.203-22.557-28.949-30.305c-25.072-9.121-40.577-22.343-40.577-43.759c0-23.93,19.829-41.708,49.688-41.708
c15.495,0,27.112,3.646,33.719,7.516l-5.456,16.182c-4.787-2.959-15.031-7.293-28.949-7.293c-20.961,0-28.94,12.536-28.94,23.021
c0,14.354,9.344,21.425,30.536,29.627c25.981,10.03,38.971,22.565,38.971,45.123c0,23.717-17.313,44.444-53.557,44.444
c-14.809,0-30.991-4.546-39.194-10.039L68.836,146.216z"/>
<path fill="none" d="M82.734,183.337v-66.265L33.15,27.158h23.17l22.009,43.104c5.792,11.811,10.66,21.321,15.528,32.207h0.462
c4.17-10.207,9.736-20.396,15.764-32.207l22.473-43.104h22.707l-52.131,89.669v66.51H82.734z"/>
</svg>
</body> </body>
</html> </html>

225
booleanTests.js Normal file
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paper.install(window);
function runTests() {
var caption, pathA, pathB;
var container = document.getElementById( 'container' );
caption = prepareTest( 'Overlapping circles', container );
pathA = new Path.Circle(new Point(80, 110), 50);
pathB = new Path.Circle(new Point(150, 110), 70);
testBooleanStatic( pathA, pathB, caption );
caption = prepareTest( 'Disjoint circles', container );
pathA = new Path.Circle(new Point(60, 110), 50);
pathB = new Path.Circle(new Point(170, 110), 50);
testBooleanStatic( pathA, pathB, caption );
caption = prepareTest( 'Overlapping circles - enveloping', container );
pathA = new Path.Circle(new Point(110, 110), 100);
pathB = new Path.Circle(new Point(120, 110), 60);
testBooleanStatic( pathA, pathB, caption );
caption = prepareTest( 'Polygon and square', container );
pathA = new Path.RegularPolygon(new Point(80, 110), 12, 80);
pathB = new Path.Rectangle(new Point(100, 80), [80, 80] );
testBooleanStatic( pathA, pathB, caption );
caption = prepareTest( 'Circle and square (overlaps exactly on existing segments)', container );
pathA = new Path.Circle(new Point(110, 110), 80);
pathB = new Path.Rectangle(new Point(110, 110), [80, 80] );
testBooleanStatic( pathA, pathB, caption );
caption = prepareTest( 'Circle and banana (multiple intersections within same curve segment)', container );
pathA = new Path.Circle(new Point(80, 110), 80);
pathB = new Path.Circle(new Point(130, 110), 80 );
pathB.segments[3].point = pathB.segments[3].point.add( [ 0, -120 ] );
testBooleanStatic( pathA, pathB, caption );
caption = prepareTest( 'Overlapping stars 1', container );
pathA = new Path.Star(new Point(80, 110), 10, 20, 80);
pathB = new Path.Star(new Point(120, 110), 10, 30, 100);
testBooleanStatic( pathA, pathB, caption );
caption = prepareTest( 'Overlapping stars 2', container );
pathA = new Path.Star(new Point(110, 110), 20, 20, 80);
pathB = new Path.Star(new Point(110, 110), 6, 30, 100);
testBooleanStatic( pathA, pathB, caption );
caption = prepareTest( 'Circles overlap exactly over each other', container );
pathA = new Path.Circle(new Point(110, 110), 100);
pathB = new Path.Circle(new Point(110, 110), 100 );
testBooleanStatic( pathA, pathB, caption );
caption = prepareTest( 'Maximum possible intersections between 2 cubic bezier curve segments - 9', container );
pathA = new Path();
pathA.add( new Segment( [173, 44], [-281, 268], [-86, 152] ) );
pathA.add( new Segment( [47, 93], [-89, 100], [240, -239] ) );
pathA.closed = true;
pathB = pathA.clone();
pathB.rotate( -90 );
// FIXME: hangs when I move pathA, pathB apart by [-10,0] & [10,0] or [9...] etc.
pathA.translate( [-11,0] );
pathB.translate( [11,0] );
testBooleanStatic( pathA, pathB, caption );
annotatePath( pathA, null, '#008' );
annotatePath( pathB, null, '#800' );
view.draw();
caption = prepareTest( 'Glyphs imported from SVG', container );
var group = paper.project.importSvg( document.getElementById( 'glyphsys' ) );
pathA = group.children[0];
pathB = group.children[1];
testBooleanStatic( pathA, pathB, caption );
function prepareTest( testName, parentNode ){
console.log( '\n' + testName );
var caption = document.createElement('h3');
caption.appendChild( document.createTextNode( testName ) );
var canvas = document.createElement('CANVAS');
parentNode.appendChild( caption );
parentNode.appendChild( canvas );
paper.setup( canvas );
return caption;
}
}
var booleanStyle = {
fillColor: new Color( 1, 0, 0, 0.5 ),
strokeColor: new Color( 0, 0, 0 ),
strokeWidth: 2
};
var pathStyleNormal = {
strokeColor: new Color( 0, 0, 0 ),
fillColor: new Color( 0, 0, 0, 0.0 ),
strokeWidth: 1
};
var pathStyleBoolean = {
strokeColor: new Color( 0.8 ),
fillColor: new Color( 0, 0, 0, 0.0 ),
strokeWidth: 1
};
// Better if path1 and path2 fit nicely inside a 200x200 pixels rect
function testBooleanStatic( path1, path2, caption ) {
try{
var _p1U = path1.clone().translate( [280, 0] );
var _p2U = path2.clone().translate( [280, 0] );
console.time( 'Union' );
var boolPathU = boolUnion( _p1U, _p2U );
console.timeEnd( 'Union' );
var _p1I = path1.clone().translate( [560, 0] );
var _p2I = path2.clone().translate( [560, 0] );
console.time( 'Intersection' );
var boolPathI = boolIntersection( _p1I, _p2I );
console.timeEnd( 'Intersection' );
path1.style = path2.style = pathStyleNormal;
_p1U.style = _p2U.style = _p1I.style = _p2I.style = pathStyleBoolean;
boolPathU.style = boolPathI.style = booleanStyle;
} catch( e ){
console.error( e.message );
if( caption ) { caption.className += ' error'; }
paper.project.view.element.className += ' hide';
} finally {
console.timeEnd( 'Union' );
console.timeEnd( 'Intersection' );
view.draw();
}
}
// ==============================================================
// On screen debug helpers
function markPoint( pnt, t, c, tc, remove ) {
if( !pnt ) return;
c = c || '#000';
if( remove === undefined ){ remove = true; }
var cir = new Path.Circle( pnt, 2 );
cir.style.fillColor = c;
cir.style.strokeColor = tc;
if( t !== undefined || t !== null ){
var text = new PointText( pnt.add([0, -3]) );
text.justification = 'center';
text.fillColor = c;
text.content = t;
if( remove ){
text.removeOnMove();
}
}
if( remove ) {
cir.removeOnMove();
}
}
function annotatePath( path, t, c, tc, remove ) {
if( !path ) return;
var crvs = path.curves;
for (i = crvs.length - 1; i >= 0; i--) {
annotateCurve( crvs[i], t, c, tc, remove );
}
var segs = path.segments;
for (i = segs.length - 1; i >= 0; i--) {
annotateSegment( segs[i], t, c, tc, remove, true );
}
}
function annotateSegment( s, t, c, tc, remove, skipCurves ) {
if( !s ) return;
c = c || '#000';
tc = tc || '#ccc';
t = t || s.index;
if( remove === undefined ){ remove = true; }
var crv = s.curve;
var t1 = crv.getNormal( 0 ).normalize( 10 );
var p = s.point.clone().add( t1 );
var cir = new Path.Circle( s.point, 2 );
cir.style.fillColor = c;
cir.style.strokeColor = tc;
var text = new PointText( p );
text.justification = 'center';
text.fillColor = c;
text.content = t;
if( remove ) {
cir.removeOnMove();
text.removeOnMove();
}
if( !skipCurves ) {
annotateCurve( s.curveIn, null, c, tc, remove );
annotateCurve( s.curveOut, null, c, tc, remove );
}
}
function annotateCurve( crv, t, c, tc, remove ) {
if( !crv ) return;
c = c || '#000';
tc = tc || '#ccc';
t = t || crv.index;
if( remove === undefined ){ remove = true; }
var p = crv.getPoint( 0.57 );
var t1 = crv.getTangent( 0.57 ).normalize( -10 );
var p2 = p.clone().add( t1 );
var l = new Path.Line( p, p2 ).rotate( 30, p );
var l2 = new Path.Line( p, p2 ).rotate( -30, p );
p = crv.getPoint( 0.43 );
var cir = new Path.Circle( p, 8 );
var text = new PointText( p.subtract( [0, -4] ) );
text.justification = 'center';
text.fillColor = tc;
text.content = t;
l.style.strokeColor = l2.style.strokeColor = cir.style.fillColor = c;
if( remove ) {
l.removeOnMove();
l2.removeOnMove();
cir.removeOnMove();
text.removeOnMove();
}
}

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